Question

Concider the set A ={1,4,7,10, 13,16... 97,100}. All subsets of A having N elaments have the property that there are two elements in the set whose sum is 104. Find the minimum value of N​

Answer 1

The minimum value of N​ is 16

Given : A = {1, 4, 7, 10, 13, 16___97, 100}.

All subsets of A having N elements have the property that there are two elements in the set whose sum is 104.

To Find :  Value of N

Solution:

A   = {1, 4, 7, 10, 13, 16___97, 100}

form is 3n+ 1   where n is integer from 0 to  33  

Let say two element are 3p+1  , 3q+1  where p , q ∈ n

3p+1 + 3q + 1  = 104

3(p + q)  = 102

=> p + q  =  34

p = 1  , q = 33     ( 4 , 100)

p = 2   q  = 32    (7 , 97)

p = 15  q = 19   ( 46  , 58)

p = 16  q = 18    ( 49 , 55)

Hence there are 16 sets having  the property that there are two elements in the set whose sum is 104

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Answer 2

Answer:

104

Step-by-step explanation:

by observation ^^^^^